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Tilting Styx and Nix but not Uranus with a Spin-Precession-Mean-motion resonance

  • Alice C. QuillenEmail author
  • Yuan-Yuan Chen
  • Benoît Noyelles
  • Santiago Loane
Original Article
First Online:

Abstract

A Hamiltonian model is constructed for the spin axis of a planet perturbed by a nearby planet with both planets in orbit about a star. We expand the planet–planet gravitational potential perturbation to first order in orbital inclinations and eccentricities, finding terms describing spin resonances involving the spin precession rate and the two planetary mean motions. Convergent planetary migration allows the spinning planet to be captured into spin resonance. With initial obliquity near zero, the spin resonance can lift the planet’s obliquity to near 90\(^\circ \) or 180\(^\circ \) depending upon whether the spin resonance is first or zeroth order in inclination. Past capture of Uranus into such a spin resonance could give an alternative non-collisional scenario accounting for Uranus’s high obliquity. However, we find that the time spent in spin resonance must be so long that this scenario cannot be responsible for Uranus’s high obliquity. Our model can be used to study spin resonance in satellite systems. Our Hamiltonian model explains how Styx and Nix can be tilted to high obliquity via outward migration of Charon, a phenomenon previously seen in numerical simulations.

Keywords

Planets and satellites: dynamical evolution and stability Celestial Mechanics Planets and satellites: individual: Styx Planets and satellites: individual: Nix 
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Notes

Acknowledgements

We warmly thank our referee, Gwenaël Boué, for kindly finding and helping us correct our errors. His time is very much appreciated. We gratefully acknowledge support from the Simons Foundation and the hospitality of the Leibniz Institut für Astrophysik, Postdam. BN acknowledges the financial support of the contract Prodex CR90253 from the Belgian Science Policy Office. This work is supported by the National Natural Science Foundation of China (grants 11403107) and the Natural Science Foundation of Jiangsu Province (grant BK20141045).

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Physics and AstronomyUniversity of RochesterRochesterUSA
  2. 2.Key Laboratory of Planetary Sciences, Purple Mountain ObservatoryChinese Academy of SciencesNanjingChina
  3. 3.Department of Mathematics, Namur Centre for Complex Systems (naXys)University of NamurNamurBelgium

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